In iPhone Settings -> Mail, Contacts, Calendars -> Contacts, there is a message:
New contacts created outside of a specific account will be added to this account.
What does that specific account referring to?
IPhone – What does iPhone new contacts “outside of specific account” mean
contactsdata synchronizationgoogle-synciphone
Related Solutions
Each Mail account on your iOS 4+ device is able to sync notes. When you have it enabled for multiple mail accounts you're able to have notes stored in different accounts. The Default Account setting will be for which account the notes are associated with unless you say so otherwise (Identical to the Default mail account in terms of functionality). The screenshot below might help - namely showing the Notes app is like the Mail application - an All Notes (Mail) view and just viewing on the individual accounts.
I haven't had an opportunity to test this out, but I'm pretty sure that the iPhone silos contacts on a per-account basis. When you set up a CardDAV or Exchange account in Settings, it's unique from anything else. The contacts don't intermingle, beyond showing up in the same app.
You can think of it like having two different email accounts that your phone checks. You can access both, they'll even show up in a unified inbox, but emails in a folder on one account don't get synced to a folder on the other account.
Off the top of my head, to synchronize the two accounts, you'd probably need an app running on a computer that could synchronize between the two, and then connect your phone to either the CardDAV or Exchange server as the canonical version.
Best Answer
This happens if you also have your iPhone setup to sync to outlook via a microsoft exchange server.
The key here is to setup your "default account" to also work the same way when you are manually adding contacts to your iPhone.
Under Settings -> Mail, Contacts, Calendars -> Contacts -> Default Account you can select an account to have your contacts created in when you create a new contact.
"outside of a specific account" refers to your exchange account setup.
If you have any issues where contacts created on your iPhone don't sync correctly with your exchange account then you should change the default account to point to your exchange account.
more info and discussion about this (as well as potential sync issues with exchange server) can be found here.
Hope this helps.